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His garage looked like a meth lab. Funnels and siphons littered the floor. Jars of viscous liquids, stacked precariously, lined the walls. The smell of citrus suffused the air.

Driving into the city after preparing cavatelli with pork ragù for a local TV show, Alon Shaya, the chef at Domenica(Roosevelt Hotel, 123 Baronne St.; 504-648-6020; domenicarestaurant.com) in New Orleans, tells me the story of the alcoholic elementary-school crossing guard in Colorno, Italy, who taught him how to make limoncello.

His secret, Shaya says, was to wrap whole lemons in cheesecloth and hammock them in a half-filled jar of grain alcohol with a closed lid. In time, the alcohol cyclically evaporated and condensed, leaching the essential oils from the lemons. After two months, the lemons were ghost white. And the liquid bloomed with a citrus bouquet.

Most limoncello recipes dictate the peeling of lemons and the avoidance of their pith, which can embitter the liqueur. But Shaya—a tall 33-year-old born in a Tel Aviv suburb, reared in Philadelphia and educated at the Culinary Institute of America—discovered a better way during a ten-month gambol through Italy.

Every serious American chef working the Italian rubric now makes an inspirational trek to Italy. They travel to Parma and have epiphanies while perfecting the craft of prosciutto. In Veneto, they scoff at the red sauce joints of their childhood while stirring al dente risottos. After a week in Liguria, they defend mortar-and-pestle pesto from the stateside infidels who believe food processors can achieve a proper emulsion.

Shaya was 28 when he made that trek. In the small towns of Parma, he worked unpaid stages and reveled in hard-won moments of clarity, like the time, on a pilgrimage to the estate of Giuseppe Verdi, he learned that the late composer was a fellow Louisiana obsessive, who once dug a faux bayou and planted real cypress trees on the grounds.

He returned to New Orleans with all manner of new techniques in his quiver: how to cure the perfect culatello; or how much pressure to apply to the dough when punching out anolini.

More important, in the four years since he opened Domenica with his partners, chef John Besh and restaurateur Octavio Mantilla, Shaya has leveraged that time in Italy, as well as his subsequent returns to Israel, to hone a very personal cuisine that reflects his adopted homeland of Parma, his familial homeland of Tel Aviv and New Orleans, America’s papal city of food and drink.

If that combination of cultures sounds dissonant, then you haven’t booked a Sunday night table at Domenica, a soaring ebony and chrome restaurant where the stock-in-trade is fire-blistered pizzas draped with house-made mortadella.

When I take my seat, Morgan Freeman is hunkered in the back corner, enjoying his third dinner there in two weeks, smiling slyly and spooning long strands of squid-ink pasta and fat lumps of crab into baroque coils. A few tables closer to the center of the room—in sight of a glass-fronted salumi case, beneath a crystal chandelier dripping with baubles that resemble the snail-shaped pasta called lumache—Nancy Oakes, proprietor of the beloved San Francisco restaurant Boulevard, anchors a boisterous table, where she forks into a Louisiana redfish fillet, doused in a warm olive vinaigrette.

None of the 400 diners who pass through Domenica this night seem to eye the celebrities. Instead, they devour corduroy-textured garganelli pasta heaped with a ragù of mangalitsa pork and rapini greens; haunches of wood-roasted goat, served shakshouka style, in a sauce of tomatoes and yard eggs; heirloom sweet potatoes slathered with rosemary butter and painted with Louisiana cane syrup. All are in the full thrall of Shaya. They are inhaling his worldview. They are adopting his homelands as their own.

It had not always been this way. When Domenica opened in 2009, customers demanded checkered-tablecloth standards. “They wanted their red sauce; they wanted their white sauce,” Shaya tells me as we taste new menu ideas. “They said the meatballs were too small.”

Under the tutelage of Besh, whose New Orleans restaurant empire now employs 650 people, Shaya learned to keep his head down and serve it forth.

Before he became a chef, Shaya had faced much worse. He was just four when he and his mother and sister emigrated from Israel to Philadelphia. By 12, he was a bit of a rebel. At 16, he stole his mother’s baby-blue Ford Taurus and drove it to Atlantic City.

He didn’t find his people until he took a home-economics class. “All the other tenth-graders were baking chocolate-chip cookies, and I was making linguini with clam sauce,” Shaya says as his Domenica colleagues prep for Monday dinner beneath a clock with a face that reads “Take the time to make it SUPER BAD ASS.”

Daily life in New Orleans came easier for Shaya, who was 23 when Mantilla recruited him to serve as chef at Besh Steakhouse. This is my home, Shaya told himself, when the woman who would become his wife lured him from work one Saturday night to see the Rebirth Brass Band play a Frenchmen Street atelier.

The city gave of itself. And Shaya gave himself to the city.

After Hurricane Katrina, Shaya cooked pots of red beans and rice for emergency workers in St. Bernard Parish. When volunteers arrived to rebuild Willie Mae’s Scotch House—the Treme fried-chicken citadel—he led the crew from Besh’s restaurant group, who were serving all workers from silver chafing dishes on white linen–draped tables positioned in the wreckage-strewn street.

Through the years, Shaya has studied the city and applied that knowledge to his cookery. Domenica’s early menus were comparatively hidebound—and mostly Italian. But that changed as Shaya came to claim this place.

Asked to cook for special events, he began to conceive narratives, not just menus. “I take a story, a tradition, and try to make it relevant,” Shaya says as we graze his bookshelves, stacked with two editions of The Classic Cuisine of the Italian Jews, and I recall a brunch he cooked last year to honor Sicilian immigrants who arrived in 1880s New Orleans.

Travel broadened his worldview: With the Jewish Federation, Shaya journeyed to Israel, where his father had fought in the Yom Kippur War. Near Tel Aviv he cooked gumbo for a gathering of Yemenite Jews; and in the Golan Heights he baked an almond cake for Israeli servicemen.

Inspired, Shaya now hosts Passover Seders for customers. His approach is hardly kosher. Shaya bakes the matzo in the same pecan wood–fired oven where tutto carne pizzas—scattered with sausage and bacon—achieve their crusts. But it’s honest. And it reflects his passport stamps. The most talked-about dish on the regular menu—cauliflower, roasted whole, served beside a slick of whipped goat feta—was inspired by that trip to Tel Aviv, where Shaya ate a similar dish.

Like Andrea Reusing, who cooks Asian dishes with local ingredients in Chapel Hill, North Carolina, and Tyson Cole, who built a temple to sushi in Austin, Texas, Shaya—a 2012 James Beard Award finalist for best chef in the South—has earned freedom from the provincial dictates of regional cuisine.

His food stokes local pride. (Shaya calls his torta fritta, which he cooks in lard, beignets.) And his food is worldly enough to engage the more adventurous. (He occasionally serves his crew lobes of sea urchin atop those beignets.)

For diners who cultivate knowledge of this bright, brackish gumbo of a city, Domenica, circa now, tastes like an important next step. And Shaya, the limoncello savant, thinks and cooks like the ascendant conjurer of New Orleans’ grand culinary traditions.

What’s Cooking at Domenica

Originality with respect for tradition is evident in these five dishes.

Spicy Lamb Meatball Pizza: For his ricotta, Shaya uses a “hair sheep” breed from Two Run Farm, just across the border in Mississippi.